The Australian captain hasn’t trained since touching down in Abu Dhabi on Saturday, and is in severe doubt for the match.
The camp hasn’t given details of the injury, with Jedinak describing it as a knock from Thursday night’s 2-0 win over Iraq.
Postecoglou has until two hours before the 7:30pm kickoff (1:30am Wednesday Adelaide time) to submit his squad for the UAE match and told reporters he would take any decision down to the wire.
“We’ll give him every chance to recover and see whether he’s available on game day,” he said.
“When we’re in camp we understand things even happen on game day where we need to change the line up. That’s happened in the past and no one’s even known about it.
“We’re hoping he’ll be ok but if he’s not then we’ll be able to bring in somebody else to do the job.”
Mark Milligan is the obvious candidate to fill Jedinak’s boots, but the 31-year-old was deployed usefully in defence against Iraq.
If Milligan shuffled forward, Matthew Spiranovic could take up his usual place in the heart of defence.
But Postecoglou – who counts selection surprises as his stock-in-trade – could also throw Jackson Irvine into the role, or use Aaron Mooy or Massimo Luongo deeper.
All three play as sitting midfielders for their English Championship clubs.
Australia are looking for their first win in the Middle East under Postecoglou after three unsuccessful efforts.
Opposing coach Mahdi Ali said that record didn’t give his side an advantage.
“I don’t believe in history. I believe only in what the team is doing at this moment,” he said.
“I don’t know what happened before, but what I know is on the pitch the team is very well prepared.”
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